Question

A figure has been dilated from the origin by a scale factor of

of. If another dilation from the origin maps the dilated image back
onto the original figure, what is its scale factor?

Answer 1

See Explanation

Explanation:

The question has missing details. So, I'll solve using a general assumption.

Let one of the coordinates of the figure be

`A = (x,y)`

Let the scale factor be n

When dilated, the new figure is:

`A' = n * A`

`A' = n * (x,y)`

To return the image back to the original figure, the new scale factor mus be a reciprocal of the previous scale factor i.e.
`(1)/(n)`

So:

`A = A' * (1)/(n)`

Substitute n(x,y) for A';

`A = n(x,y) * (1)/(n)`

`A = (n(x,y))/(n)`

`A = (x,y)`

Take for instance:

`A = (2,3)`

`n = 2` -- scale factor

`A' = n * A`

`A' = 2 * (2,3)`

`A' = (4,6)`

To get A from A', using the analysis above

`A = (1)/(2) * (4,6)`

`A = (2,3)`